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Comment:
← Revision 38 as of 2009-05-22 13:40:01 → ⇥
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Editor: UlrikeHeiter
Comment: small correction to observed line numbers
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<<TableOfContents>>
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TiO line lists calculated by Bertrand.

'''Transitions in BP's line list:'''		 TiO line lists calculated by Bertrand on 29 May 2008.
The files are in Uppsala at /h5/plez/TiOVALD/linelist/linelist??_all.dat.gz
<<BR>>
For files with non-resolved lambda-doubled lines merged see below (under "Lambda doubling").

Number of lines:

||Isotope ||N,,merg,,||N,,orig,,||
||46 || 8193347 ||11140205 ||
||47 || 8194614 ||11141521 ||
||48 || 8195512 ||11142777 ||
||49 || 8196355 ||11143980 ||
||50 || 8197133 ||11144857 ||
||total ||40976961 ||55713340 ||

N,,orig,, ... original lists<<BR>>
N,,merg,, ... non-resolved lambda-doubled lines merged

== Transitions in BP's line list ==
Line 9: Line 27:
'''Comment on "lambda doubling" (BP, 28 Jan 2009):''' == Lambda doubling ==

-- BertrandPlez 28 Jan 2009:
Line 13: Line 33:
For some transitions Lambda-doubling does not exist (if Lambda=0, i.e if one of the states is a sigma state). For some transitions Lambda-doubling does not exist (if Lambda=0, i.e if one of the states is a Sigma state).

-- UlrikeHeiter <<DateTime(2009-02-06T10:37:27+0200)>> - Lambda-doubled lines with same wavenumbers have been merged according to BP's comment above.

The new files are in Uppsala at
/h19/ulrike/Molecules/Data/TiO/linelist??_all_nodoubling.dat.gz

The merging code is at /h19/ulrike/Molecules/Data/TiO/tio_plez_rm_doubling.pro

In the calculated lists, parity is given by the syml and symu quantum numbers, which can be 1 or -1.
In the merged lists, syml and symu are set to 0 for the merged lines.

 * lambda doubling in calculated lists in '''gamma prime system'''
  * P1,Q1,R1: lambda doubling resolved for all lines
  * P2,Q2,R2: lambda doubling resolved for J,,low,,>~10
  * P3,Q3,R3: lambda doubling resolved for J,,low,,>=3
  * "resolved" here means: wavenumber difference >=0.001
 
 * wavenumber (wn) difference for calculated lambda-doubled lines in '''gamma prime system'''
  * P1,P2,R1,R2 (all v-v):
   * for even J,,low,,: wn(syml=-1) > wn(syml=1),
   * for odd J,,low,, vice versa
  * Q1,Q2: reverse of P
   * for even J,,low,,: wn(syml=1) > wn(syml=-1),
   * for odd J,,low,, vice versa
  * PQR 3: reverse of PQR 1,2
  * for the actual values for PQR 1 and 2 see the plots below (the values are the same for each of the three v-v combinations 0-0, 1-0, 0-1), and compare to the plots for observed lambda-doubled lines further down

{{attachment:linelist48_all-H-PQR1-wn-0.png}}
{{attachment:linelist48_all-H-PQR1-wn-1.png}}
{{attachment:linelist48_all-H-PQR1-wn-2.png}}
{{attachment:linelist48_all-H-PQR1-wn-3.png}}
{{attachment:linelist48_all-H-PQR2-wn-0.png}}
{{attachment:linelist48_all-H-PQR2-wn-1.png}}
{{attachment:linelist48_all-H-PQR2-wn-2.png}}
{{attachment:linelist48_all-H-PQR2-wn-3.png}}

== Observed wavenumbers ==

A separate list with observed wavenumbers from Phillips (Bertrand Plez, priv. comm. 17 Sep 2008, 14 May 2009) and calculated other values from Plez (from the list with lambda-doubled lines merged), has been generated. Reference: Davis et al. 1986, ApJ 309, 449.

It contains lines in the alpha, beta, gamma, gamma prime systems
with range:
||wavenumber(cm^-1^) ||||wavelength(Å) ||
|| || vacuum || air ||
||20997.64 ||4762.440 || 4761.109 ||
||11383.24 ||8784.845 || 8782.433 ||

Isotope: ^48^Ti (see Davis et al. 1986, IV.a p. 452)

The original list is at /h19/ulrike/Molecules/Data/TiO/TiO-Phillips-OBS.dat and has 35584 lines.

Content:
"Obs", vupp, vlow, Jlow, "+", branch, ".0000E+00", wavenumber, ".000", system

The converted list (ascii format, same format as calculated list) is at /h19/ulrike/Molecules/Data/TiO/TiO-Phillips-OBS-vald.asc and has 35912 lines.

The conversion code is at /h19/ulrike/Molecules/Data/TiO/tio_phillips_to_vald_ascii.f

The list has been sorted by wavelength after running the conversion code.

Differences between observed and calculated wavelengths, O-C: min=-5.4Å, max=1.7Å.

Explanation for different numbers of lines in original and converted list:
 * 157 lines in systems other than gamma prime are not in the calculated list (all with J,,low,,<=4).
 * In the alpha and gamma systems, there are five "double" lines with same quantum numbers and branch names but slightly different wavenumbers. The wavenumbers for these have been averaged for the converted list. There are 18 double lines with exactly the same parameters. The duplicates have been removed for these.
 * There are 137 gamma prime P11/Q11/R11 lines, which are not in calculated list and have been discarded.
 * 290 gamma prime PQR 1/2 lines have been discarded, where only one component (C or D) is in the observed list.
 * There is a double entry for gamma prime 0-1 J,,low,,=7 R1D.
 * For 20 lines in the gamma prime P1,Q1,P2,Q2,R2 lists, lambda doubling is not resolved in the calculated list. The observed wavenumber differences are very small for these lines (<=0.05 cm-1, >0 only for four lines), therefore they have been averaged.
 * The double line gamma prime 0-1 J,,low,,=1 R2 is not in the calculated list.
 * P3,Q3,R3 lines in the gamma prime system are "double", because of resolved lambda doubling in the calculated list (+958 lines).
 * Totals: -630 +958


=== Observed lines in beta system ===

||v-v || branch || J,,low,min,, || J,,low,max,, || J,,low,, missing ||
|| || || || || ||
||0-0 || P || 4 || 99 || 94 ||
||1-1 || P || 2 || 100 || 66,88,91,92,93,95 ||
||2-2 || P || 2 || 90 || 8,10,12,14,76,81,83 ||
|| || || || || ||
||0-0 || Q || 2 || 100 || 4 ||
||1-1 || Q || 1 || 100 || 2,4,96 ||
||2-2 || Q || 3 || 100 || 7,78,82,83,84,89,90,91 ||
|| || || || || ||
||0-0 || R || 2 || 100 || ||
||1-1 || R || 2 || 98 || 7 ||
||2-2 || R || 2 || 92 || 5,26,42,62,64,70,74,75,84||

=== Observed lines in gamma prime system ===

observed lines in '''gamma prime system''', '''P1,Q1,R1''' branches (C/D pairs for each v-v and J,,low,,), J,,low,, values:
||v,,upp,,-v,,low,, || branch || J,,low,min,, || J,,low,max,, || J,,low,, missing C+D || J,,low,, missing C || J,,low,, missing D ||
|| || || || || || || ||
|| 0-0 || P1 || 3 || 131 || || 3,4,5,6,13,23 || 29,104,130,131 ||
|| 1-0 || P1 || 2 || 107 || 98 || 21,77 || 15,63,103,107 ||
|| 0-1 || P1 || 2 || 145 || 89,93,109,110,120,123 || 2,10,14,28,29,63,104, 126,131,135,138,139, 140,144,145 || 23,62,68,71,72,77,84,98, 99,111,125,129,130,136 ||
|| || || || || || || ||
|| 0-0 || Q1 || 1 || 141 || 2 || 1,12,119,138,139,140,141 || 4,7,118 ||
|| 1-0 || Q1 || 1 || 120 || || 1,104,105,112,114,118 || ||
|| 0-1 || Q1 || 2 || 144 || 94,138 || 11,104,107,114,125,127, 128,129,130,132,133,143,144 || 8,77,100,102,122,124 ||
|| || || || || || || ||
|| 0-0 || R1 || 1 || 122 || 96 || 5,6,19,64,87 || 1,2,76,83,84,90,94,100, 107,>=110 ||
|| 1-0 || R1 || 1 || 135 || 126 || 28,43,78,82,95 || 116,119,121,128,131 ||
|| 0-1 || R1 || 1 || 150 || 119,122,124,148 || 22,58,78,87,100,105,106, 108,111,114,115,130, 137,>=144 || 5,38,39,53,81,103,116, 117,121,125,128,141 (7 double)||

observed lines in '''gamma prime system''', '''P1,Q1,R1''' branches, wavenumber differences between C and D lines:

{{attachment:TiO-Phillips-OBS-H-P1CD-wn.png}}
{{attachment:TiO-Phillips-OBS-H-Q1CD-wn.png}}
{{attachment:TiO-Phillips-OBS-H-R1CD-wn.png}}


observed lines in '''gamma prime system''', '''P2,Q2,R2''' branches (C/D pairs for each v-v and J,,low,,), J,,low,, values:
||v,,upp,,-v,,low,, || branch || J,,low,min,, || J,,low,max,, || J,,low,, missing C+D || J,,low,, missing C || J,,low,, missing D ||
|| || || || || || || || || ||
|| 0-0 || P2 ||11 || 106 || 16 || || 51, >=85 ||
|| 1-0 || P2 || 3 || 88 || || 3,4,6,15,34,35 || 5,16,82,88 ||
|| 0-1 || P2 || 5 || 90 || 7,9,13,16,85 || 60,67 || 69,71,74,76, >=84 ||
|| || || || || || || || || ||
|| 0-0 || Q2 || 7 || 107 || 28 || || >=84 ||
|| 1-0 || Q2 || 2 || 91 || || 90 || <=9, 35,74,91 ||
|| 0-1 || Q2 || 4 || 85 || 8,19,75,82,84 || 78 || 72,76,79,80,83,85 ||
|| || || || || || || || || ||
|| 0-0 || R2 ||11 || 106 || 19,27,32,83,96,97 || || 48,80, >=82 ||
|| 1-0 || R2 || 4 || 90 || || 18,36,81 || 4,5,6,8,22,25,37,41,50,61,75,89,90 ||
|| 0-1 || R2 || 1 || 91 || 88 || 18,20,67,76 || 44,48,82,83, >=85 ||

observed lines in '''gamma prime system''', '''P2,Q2,R2''' branches, wavenumber differences between C and D lines:


{{attachment:TiO-Phillips-OBS-H-P2CD-wn.png}}
{{attachment:TiO-Phillips-OBS-H-Q2CD-wn.png}}
{{attachment:TiO-Phillips-OBS-H-R2CD-wn.png}}

||v,,upp,,-v,,low,, || branch || J,,low,min,, || J,,low,max,, || wn(C)-wn(D) = delta ||
|| || || || || ||
|| 0-0 || P2 || 11 || 45 || = 0 ||
|| || || 46 || 84 || < 0 ||
|| 1-0 || P2 || 7 || 12 || |delta| < 0.07 ||
|| || || 13 || 42 || > 0 ||
|| || || 43 || 51 || |delta| < 0.07 ||
|| || || 52 || 87 || < 0 ||
|| 0-1 || P2 || 5 || 44 || = 0 (39: -0.81)||
|| || || 45 || 83 || < 0 ||
|| || || || || ||
|| 0-0 || Q2 || 7 || 44 || = 0 ||
|| || || 45 || 83 || < 0 ||
|| 1-0 || Q2 || 10 || 37 || > 0 ||
|| || || 38 || 50 || |delta| < 0.07 ||
|| || || 51 || 89 || < 0 ||
|| 0-1 || Q2 || 4 || 43 || = 0 ||
|| || || 44 || 81 || < 0 ||
|| || || || || ||
|| 0-0 || R2 || 11 || 45 || = 0 (36: +0.19)||
|| || || 46 || 81 || < 0 ||
|| 1-0 || R2 || 13 || 44 || > 0 ||
|| || || 59 || 88 || < 0 ||
|| 0-1 || R2 || 1 || 42 || = 0 ||
|| || || 43 || 84 || < 0 ||


observed lines in '''gamma prime system''', '''P3,Q3,R3''' branches:
||v,,upp,,-v,,low,, || branch || J,,low,min,, || J,,low,max,, || J,,low,, missing ||
|| || || || || ||
||0-0 || P3 || 4 || 121 || 10,14,19,31,68||
||1-0 || P3 || 7 || 95 || 63,89,93||
||0-1 || P3 || 4 || 103 || 7,19,20,52,79,82,93,97||
|| || || || || ||
||0-0 || Q3 || 11 || 130 || ||
||1-0 || Q3 || 4 || 109 || 5,10,14,17,19||
||0-1 || Q3 || 6 || 112 || 10,25,54,87,94,102,104,110||
|| || || || || ||
||0-0 || R3 || 11 || 139 || 21,25,30,65,77,118,119,123,124,134,138||
||1-0 || R3 || 5 || 124 || 99,100,103,119,122||
||0-1 || R3 || 3 || 127 || 5,14,20,70,94,95,96,98,100,113,123||

Contents

  1. TiO data
    1. Transitions in BP's line list
    2. Lambda doubling
    3. Observed wavenumbers
      1. Observed lines in beta system
      2. Observed lines in gamma prime system

TiO data

TiO line lists calculated by Bertrand on 29 May 2008. The files are in Uppsala at /h5/plez/TiOVALD/linelist/linelist??_all.dat.gz
For files with non-resolved lambda-doubled lines merged see below (under "Lambda doubling").

Number of lines:

Isotope

Nmerg

Norig

46

8193347

11140205

47

8194614

11141521

48

8195512

11142777

49

8196355

11143980

50

8197133

11144857

total

40976961

55713340

Norig ... original lists
Nmerg ... non-resolved lambda-doubled lines merged

Transitions in BP's line list

BP_transitions.png

Lambda doubling

-- BertrandPlez 28 Jan 2009:

Some transitions are affected by Lambda-doubling. In that case there are 2 sublevels that give rise to transitions, and if the separation is large enough, they appear in the list as 2 lines with the same parameters except for the parity of the upper and lower level, and a slightly different wavenumber. The degeneracy of these sublevels is 2*J+1. When the Lambda-doubling is too small there are 2 lines with exactly the same data (except the parities). One way to compact the list is to merge these lines and double the gf-value 2*(2*J+1)*f.

For some transitions Lambda-doubling does not exist (if Lambda=0, i.e if one of the states is a Sigma state).

-- UlrikeHeiter 2009-02-06 08:37:27 - Lambda-doubled lines with same wavenumbers have been merged according to BP's comment above.

The new files are in Uppsala at /h19/ulrike/Molecules/Data/TiO/linelist??_all_nodoubling.dat.gz

The merging code is at /h19/ulrike/Molecules/Data/TiO/tio_plez_rm_doubling.pro

In the calculated lists, parity is given by the syml and symu quantum numbers, which can be 1 or -1. In the merged lists, syml and symu are set to 0 for the merged lines.

  • lambda doubling in calculated lists in gamma prime system

    • P1,Q1,R1: lambda doubling resolved for all lines

    • P2,Q2,R2: lambda doubling resolved for Jlow>~10

    • P3,Q3,R3: lambda doubling resolved for Jlow>=3

    • "resolved" here means: wavenumber difference >=0.001

  • wavenumber (wn) difference for calculated lambda-doubled lines in gamma prime system

    • P1,P2,R1,R2 (all v-v):

      • for even Jlow: wn(syml=-1) > wn(syml=1),

      • for odd Jlow vice versa

    • Q1,Q2: reverse of P

      • for even Jlow: wn(syml=1) > wn(syml=-1),

      • for odd Jlow vice versa

    • PQR 3: reverse of PQR 1,2
    • for the actual values for PQR 1 and 2 see the plots below (the values are the same for each of the three v-v combinations 0-0, 1-0, 0-1), and compare to the plots for observed lambda-doubled lines further down

[ATTACH] [ATTACH] [ATTACH] [ATTACH] [ATTACH] [ATTACH] [ATTACH] [ATTACH]

Observed wavenumbers

A separate list with observed wavenumbers from Phillips (Bertrand Plez, priv. comm. 17 Sep 2008, 14 May 2009) and calculated other values from Plez (from the list with lambda-doubled lines merged), has been generated. Reference: Davis et al. 1986, ApJ 309, 449.

It contains lines in the alpha, beta, gamma, gamma prime systems with range:

wavenumber(cm-1)

wavelength(Å)

vacuum

air

20997.64

4762.440

4761.109

11383.24

8784.845

8782.433

Isotope: 48Ti (see Davis et al. 1986, IV.a p. 452)

The original list is at /h19/ulrike/Molecules/Data/TiO/TiO-Phillips-OBS.dat and has 35584 lines.

Content: "Obs", vupp, vlow, Jlow, "+", branch, ".0000E+00", wavenumber, ".000", system

The converted list (ascii format, same format as calculated list) is at /h19/ulrike/Molecules/Data/TiO/TiO-Phillips-OBS-vald.asc and has 35912 lines.

The conversion code is at /h19/ulrike/Molecules/Data/TiO/tio_phillips_to_vald_ascii.f

The list has been sorted by wavelength after running the conversion code.

Differences between observed and calculated wavelengths, O-C: min=-5.4Å, max=1.7Å.

Explanation for different numbers of lines in original and converted list:

  • 157 lines in systems other than gamma prime are not in the calculated list (all with Jlow<=4).

  • In the alpha and gamma systems, there are five "double" lines with same quantum numbers and branch names but slightly different wavenumbers. The wavenumbers for these have been averaged for the converted list. There are 18 double lines with exactly the same parameters. The duplicates have been removed for these.
  • There are 137 gamma prime P11/Q11/R11 lines, which are not in calculated list and have been discarded.
  • 290 gamma prime PQR 1/2 lines have been discarded, where only one component (C or D) is in the observed list.

  • There is a double entry for gamma prime 0-1 Jlow=7 R1D.

  • For 20 lines in the gamma prime P1,Q1,P2,Q2,R2 lists, lambda doubling is not resolved in the calculated list. The observed wavenumber differences are very small for these lines (<=0.05 cm-1, >0 only for four lines), therefore they have been averaged.

  • The double line gamma prime 0-1 Jlow=1 R2 is not in the calculated list.

  • P3,Q3,R3 lines in the gamma prime system are "double", because of resolved lambda doubling in the calculated list (+958 lines).
  • Totals: -630 +958

Observed lines in beta system

v-v

branch

Jlow,min

Jlow,max

Jlow missing

0-0

P

4

99

94

1-1

P

2

100

66,88,91,92,93,95

2-2

P

2

90

8,10,12,14,76,81,83

0-0

Q

2

100

4

1-1

Q

1

100

2,4,96

2-2

Q

3

100

7,78,82,83,84,89,90,91

0-0

R

2

100

1-1

R

2

98

7

2-2

R

2

92

5,26,42,62,64,70,74,75,84

Observed lines in gamma prime system

observed lines in gamma prime system, P1,Q1,R1 branches (C/D pairs for each v-v and Jlow), Jlow values:

vupp-vlow

branch

Jlow,min

Jlow,max

Jlow missing C+D

Jlow missing C

Jlow missing D

0-0

P1

3

131

3,4,5,6,13,23

29,104,130,131

1-0

P1

2

107

98

21,77

15,63,103,107

0-1

P1

2

145

89,93,109,110,120,123

2,10,14,28,29,63,104, 126,131,135,138,139, 140,144,145

23,62,68,71,72,77,84,98, 99,111,125,129,130,136

0-0

Q1

1

141

2

1,12,119,138,139,140,141

4,7,118

1-0

Q1

1

120

1,104,105,112,114,118

0-1

Q1

2

144

94,138

11,104,107,114,125,127, 128,129,130,132,133,143,144

8,77,100,102,122,124

0-0

R1

1

122

96

5,6,19,64,87

1,2,76,83,84,90,94,100, 107,>=110

1-0

R1

1

135

126

28,43,78,82,95

116,119,121,128,131

0-1

R1

1

150

119,122,124,148

22,58,78,87,100,105,106, 108,111,114,115,130, 137,>=144

5,38,39,53,81,103,116, 117,121,125,128,141 (7 double)

observed lines in gamma prime system, P1,Q1,R1 branches, wavenumber differences between C and D lines:

[ATTACH] [ATTACH] [ATTACH]

observed lines in gamma prime system, P2,Q2,R2 branches (C/D pairs for each v-v and Jlow), Jlow values:

vupp-vlow

branch

Jlow,min

Jlow,max

Jlow missing C+D

Jlow missing C

Jlow missing D

0-0

P2

11

106

16

51, >=85

1-0

P2

3

88

3,4,6,15,34,35

5,16,82,88

0-1

P2

5

90

7,9,13,16,85

60,67

69,71,74,76, >=84

0-0

Q2

7

107

28

>=84

1-0

Q2

2

91

90

<=9, 35,74,91

0-1

Q2

4

85

8,19,75,82,84

78

72,76,79,80,83,85

0-0

R2

11

106

19,27,32,83,96,97

48,80, >=82

1-0

R2

4

90

18,36,81

4,5,6,8,22,25,37,41,50,61,75,89,90

0-1

R2

1

91

88

18,20,67,76

44,48,82,83, >=85

observed lines in gamma prime system, P2,Q2,R2 branches, wavenumber differences between C and D lines:

[ATTACH] [ATTACH] [ATTACH]

vupp-vlow

branch

Jlow,min

Jlow,max

wn(C)-wn(D) = delta

0-0

P2

11

45

= 0

46

84

< 0

1-0

P2

7

12

|delta| < 0.07

13

42

> 0

43

51

|delta| < 0.07

52

87

< 0

0-1

P2

5

44

= 0 (39: -0.81)

45

83

< 0

0-0

Q2

7

44

= 0

45

83

< 0

1-0

Q2

10

37

> 0

38

50

|delta| < 0.07

51

89

< 0

0-1

Q2

4

43

= 0

44

81

< 0

0-0

R2

11

45

= 0 (36: +0.19)

46

81

< 0

1-0

R2

13

44

> 0

59

88

< 0

0-1

R2

1

42

= 0

43

84

< 0

observed lines in gamma prime system, P3,Q3,R3 branches:

vupp-vlow

branch

Jlow,min

Jlow,max

Jlow missing

0-0

P3

4

121

10,14,19,31,68

1-0

P3

7

95

63,89,93

0-1

P3

4

103

7,19,20,52,79,82,93,97

0-0

Q3

11

130

1-0

Q3

4

109

5,10,14,17,19

0-1

Q3

6

112

10,25,54,87,94,102,104,110

0-0

R3

11

139

21,25,30,65,77,118,119,123,124,134,138

1-0

R3

5

124

99,100,103,119,122

0-1

R3

3

127

5,14,20,70,94,95,96,98,100,113,123

ValdWiki: TiO (last edited 2012-05-04 17:16:40 by UlrikeHeiter)